Question: Simplify the following expression: $ a = \dfrac{4}{7} + \dfrac{-9}{5t + 2} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5t + 2}{5t + 2}$ $ \dfrac{4}{7} \times \dfrac{5t + 2}{5t + 2} = \dfrac{20t + 8}{35t + 14} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{-9}{5t + 2} \times \dfrac{7}{7} = \dfrac{-63}{35t + 14} $ Therefore $ a = \dfrac{20t + 8}{35t + 14} + \dfrac{-63}{35t + 14} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{20t + 8 - 63}{35t + 14} $ $a = \dfrac{20t - 55}{35t + 14}$